Research On The Boundedness Of Solutions For Two Classes Of Nonlinear Chemotaxis-Haptotaxis Models

In this paper,we study the boundedness of solutions of two kinds of chemotaxis-haptotaxis model with nonlinear Logistic source and nonlinear production.In Chapter 1,we introduce the research background of related Keller-Segel model and chemotaxis-haptotaxis model,as well as the research situation at home and abroad.In Chapter 2,we deal with the boundedness of solutions to the following quasilinear chemotaxis-haptotaxis model of parabolic-parabolic-ODE type:#12 under zero-flux boundary conditions in a smooth bounded domain ?(?)Rn(n?2),with parameters r?2,?>0,?>0,?>0.D(u)is assumed to satisfy D(u)??u-?,D(0)>0 for all u>0 with some ??R and ?>0,and g(u)is assumed to satisfy g(u)=u? for all u>0 with some ??q(0,1].This Chapter mainly used Lp-estimation and Moser-Alikakos iteration,and proved that if ?<n+2-2n?/2+n,then,for sufficiently smooth initial data(u0,v0,w0),the corresponding initial-boundary problem possesses a unique global-in-time classical solution which is uniformly bounded.In Chapter 3,we consider the boundedness of solutions to the following nonlinear chemotaxis-haptotaxis model:#12 under zero-flux boundary conditions in a smooth bounded domain ?(?)Rn(n?2),with parameters r?2,?>0,?>0.S(u)is assumed to satisfy S(u)??u?,S(0)>0 for all u>0 with some,??R and p>0,and g(u)is assumed to satisfy g(u)=u? for all u>0 with some ??(0,1].This Chapter mainly used Lp-estimation and Moser-Alikakos iteration,and proved that if ?<3/2-n?/2+n,then for sufficiently smooth initial data(u0,v0,w0),the corresponding initial-boundary problem possesses a unique classical solution which is global in time and bounded.In Chapter 4,we summarize the main results of the paper and proposes further problems to be done.